Notes on aplications of the dual fountain theorem to local and nonlocal elliptic equations with variable exponent

Abstract

Using the Dual Fountain Theorem we obtain some existence of infinitely many solutions for local and nonlocal elliptic equations with variable exponent. Our results correct some of the errors that have appeared recently in the literature.

Keywords

• dual fountain theorem
• \(p(\cdot)\)-laplacian
• fractional \(p(\cdot)\)-laplacian
• infinitely many solutions